Can you shuffle an album in the numerical order it appears on in the original track listing? Like, let’s say the album has 14 songs, statistically, if you shuffle enough times then the order of the songs would appear in the track list order, no?
In: 3
Or is there a mechanism in the software that prevents this?
Well, yes and no. For an album with 14 songs, if you reshuffled once per second, without stopping to sleep or for any other reason, it would take on average about 1400 years before you got the lucky hit. (14! seconds is about 2700 years.) Thus, unless you are very lucky, it won’t happen for you. If everyone on Earth started doing it, the first hit would happen pretty quickly.
For an album with only 10 songs, you’d average a hit in 21 days. (10! seconds is about 42 days.) Even taking breaks for sleep and food, that’s unpleasant, but do-able.
Theoretically – yes. If you have a fourteen-track album, you have a 1/14 chance of song number one being played first, a 1/13 chance of song number two being played second, etc. The odds are low though – for a 14-track album, the odds are 1/14!, or 1 in 87,178,291,200.
That said, the shuffle algorithm may prevent this from happening, as the point of shuffle is to _not_ have the songs play in album order.
The number of different ways to order N-many items can be calculated using something called “N-factorial” which is written as “N!”.
For three songs, that is three-factorial 3! many ways, and the definition of factorial means that this equals 3!=3x2x1=6 ways to order the songs… so randomly shuffling to the correct order would occur 1/6 of the time (about 16.7% of the time).
For four songs, 4!=4x3x2x1=24 so shuffling into the correct order has a 1/24 chance of happening (4.2% chance).
For five songs, 5!=5x4x3x2x1=120… so 1/120 (0.8%).
…For 14 songs, that 14!=14x13x12x11x10x9x8x7x6x5x4x3x2x1=87,178,291,200 amounts to ~87-Billion… so 1/87178291200 is crazy small.
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As for “Why does the factorial math describe the number of ways to shuffle something?” you gotta think about it in reverse.
There’s only one place to put the first song. 1
You can put the second song either before or after that. (1)x2
You can put the third song either before the other two, in between, or after. (1×2)x3
And so on!
If you had a completely randomised shuffle then theoretically yes, you would expect this to occur about once every 87 billion shuffles (the total number of different ways you can sequence 14 titles) (so realistically for most people, not even once their entire life time), however no shuffle algorithm in common usage actually IS completely randomised.
This is because when humans shuffle something they don’t actually want a truly random order, they want a diverse order. In a completely random shuffle you would expect some short sequences of similar/correctly ordered songs to appear quite often, and humans don’t want those to happen at all when they shuffle something, so the vast majority of shuffle algorithms isn’t actually truly random, but skews the results to prevent/reduce any short patterns occurring in the shuffled order, so for most real shuffle algorithms, it’s not just vanishingly unlikely, it’ll be completely impossible
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How I always put it in perspective is that, yes there’s 1 in 87B chance of that happening (described in another reply) but any specifically chosen order, say one that appears random, has exactly the same chance of appearing.
It’s a bit mind blowing to realise that chosing 1,2,3,4,5,6,7 as your lottery numbers has the exact same chance of winning as chosing 3,8,17,18,26,33,42 (or whatever the winning combo was). But we wouldn’t choose a sequence like that would we?
It depends on how we implement the idea of “shuffle”.
If you treat the tracks like a deck of cards, put them in a random order, then start playing them in that order then yes, you can end up with a shuffled play order that mimics the original order.
If you *on purpose* pick any track but the first one, THEN make a list of the remaining ones, shuffle that list, and play that order, then you might get “almost the original order” but you’ll never get “the original order”.
Writing a shuffle that *never* puts more than two or three tracks in the “right” order is pretty tough to describe, but possible. For how small most albums are you could probably do a shuffle, check if it’s “wrong”, and just try again if it’s “wrong”.
But all of these are “a shuffle”. So the trick here is you have to know *how* you’re shuffling to know if it’s possible to get the original track list.
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